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Physics linear velocity to angular velocity, textbook wrong?

 
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tmlrules



Joined: 26 Nov 2010
Posts: 2
Location: canada

PostPosted: Fri Nov 26, 2010 9:16 pm    Post subject: Physics linear velocity to angular velocity, textbook wrong? Reply with quote

Hi
Consider a race car that moves with a speed of 200mi/h. If it travels on circular race track of circumference 2.5 mi, what is the cars angular velocity?

First convert to meters/second and meters

Then the way I tried to solve was to find the raduis from the circumference.
c=(2pi)(r)
r=(c)/(2pi)
r=4023m/2pi
r=640m

Then
v=wr
w=v/r
w=89.4 m/s / 640m
w=0.139 rads/s which is angular velocity

But the textbook got 0.022 rads/s
they did w=v/r
but they used the full circumference 4023 meters
w=89.4 m/s / 4023m
w=0.022 rads/s

Why would they use the full circumference, when the raduis is supposed to be used? Thank you for answering, this is driving me crazy
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hepcj
Site Admin


Joined: 23 Jun 2007
Posts: 125

PostPosted: Sun Nov 28, 2010 12:24 pm    Post subject: Reply with quote

I think that it is a mistake in the book. It should be v = r w. How you have done the problem is correct. It is not uncommon for a few mistakes to find there way into the answers, but it should have been checked.
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tmlrules



Joined: 26 Nov 2010
Posts: 2
Location: canada

PostPosted: Sun Nov 28, 2010 8:42 pm    Post subject: Thanks Reply with quote

Thank you very much Very Happy . I got the same answer in two different ways, but I could not be sure if it was correct because of the answers in the back of the book.
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